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A190114
Numbers with prime factorization p^2*q^2*r^5 where p, q, and r are distinct primes.
1
7200, 14112, 24300, 34848, 39200, 47628, 48672, 83232, 96800, 103968, 112500, 117612, 135200, 152352, 164268, 189728, 231200, 242208, 264992, 276768, 280908, 288800, 297675, 350892, 394272, 423200, 453152, 484128, 514188, 532512, 566048
OFFSET
1,1
FORMULA
Sum_{n>=1} 1/a(n) = P(2)^2*P(5)/2 - P(2)*P(8)/2 - P(4)*P(5)/2 - P(2)*P(7) + P(9) = 0.00053812627050585644544..., where P is the prime zeta function. - Amiram Eldar, Mar 07 2024
MATHEMATICA
f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 2, 5}; Select[Range[900000], f]
With[{upto=600000}, Select[#[[1]]^2 #[[2]]^2 #[[3]]^5&/@ Flatten[ Permutations/@ Subsets[Prime[Range[Ceiling[Surd[upto, 5]+1]]], {3}], 1]// Union, #<=upto&]] (* Harvey P. Dale, Jul 29 2018 *)
PROG
(PARI) list(lim)=my(v=List(), t1, t2); forprime(p=2, (lim\36)^(1/5), t1=p^5; forprime(q=2, sqrt(lim\t1), if(p==q, next); t2=t1*q^2; forprime(r=q+1, sqrt(lim\t2), if(p==r, next); listput(v, t2*r^2)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 20 2011
KEYWORD
nonn
AUTHOR
STATUS
approved